Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finitely additive supermartingales are differences of martingales and adapted increasing processes


Author: Thomas E. Armstrong
Journal: Proc. Amer. Math. Soc. 95 (1985), 619-625
MSC: Primary 60G44; Secondary 60G07
DOI: https://doi.org/10.1090/S0002-9939-1985-0810174-8
MathSciNet review: 810174
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that any nonnegative bounded supermartingale admits a Doob-Meyer decomposition as a difference of a martingale and an adapted increasing process upon appropriate choice of a reference probability measure which may be only finitely additive.


References [Enhancements On Off] (What's this?)

  • [T] E. Armstrong [1983], Finitely additive $ F$-processes, Trans. Amer. Math. Soc. 279, 271-295. MR 704616 (85a:60052)
  • [K] A. Astbury [1981], Order convergence of martingales in terms of countably additive and purely finitely additive martingales, Ann. Probab. 9, 226-275. MR 606988 (82c:60081)
  • [S] Bochner and R. S. Phillips [1941], Additive set functions and vector lattices, Ann. of Math. 42, 316-324. MR 0004079 (2:315d)
  • [C] Dellacheire and P. Meyer [1982], Probabilities and potential $ B$, Theory of Martingales, North-Holland, Amsterdam. MR 745449 (85e:60001)
  • [A] Gut and K. D. Schmidt [1983], Amarts and set function processes, Springer-Verlag, Berlin. MR 727477 (85k:60064)
  • [J] Memin [1980], Espaces de semi-martingales et changement de probabilité, Z. Wahrsch. Verw. Gebiete 52, 9-39. MR 568256 (81h:60076)
  • [J] -F. Mertens [1972], Théorie des processus stochastiques generaux applications aux supermartingales, Z. Warsch. Verw. Gebiete 22, 45-68. MR 0346895 (49:11616)
  • [M] Metivier and J. Pellaumail [1975], On Doleans-Föller measure for quasi-martingales, Illinois J. Math. 19, 491-504. MR 0394860 (52:15659)
  • [P] A. Meyer [1966], Probability and potential, Blaisdell, Waltham, Mass.
  • [K] M. Rao [1969a], On decomposition theorems of Meyer, Math. Scand. 24, 66-78. MR 0275510 (43:1264)
  • 1. -[1969b], Quasi-martingales, Math. Scand. 24, 79-92. MR 0275511 (43:1265)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G44, 60G07

Retrieve articles in all journals with MSC: 60G44, 60G07


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0810174-8
Keywords: Martingale, supermartingale, increasing process, finitely additive measure, set function process
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society